Numerical Simulations of Nonlinear Modes in Mica: Past, Present and Future

Bajars, Janis; Eilbeck, J. C.; Leimkuhler, Benedict

doi:10.1007/978-3-319-21045-2_2

Cited by 25 publications

(17 citation statements)

References 23 publications

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“…Moving breathers in models inspired by the tracks in muscovite have been found in one dimension [29] using a sinusoidal on-site potential and Morse interaction and in two dimensions [30][31][32] also using sinusoidal on-site potential and either piecewise or Lennard-Jones interaction potential. The lifetime of the moving breathers was large but no physical magnitudes as the energy were provided, making it difficult to relate with the experiments.…”

Section: Introductionmentioning

confidence: 99%

Pterobreathers in a model for a layered crystal with realistic potentials: Exact moving breathers in a moving frame

2019

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In this article we perform a thorough analysis of breathers in a one-dimensional model for a layered silicate for which there exists fossil and experimental evidence of moving excitations along the close-packed lines of the K + layers. Some of these excitations are likely breathers with a small energy of about 0.2 eV as the numerically obtained breathers described in the present model. Moving breathers as exact solutions of the dynamical equations are obtained at the price of being generically associated with a plane wave, a wing, with finite amplitude, although this amplitude can be very small. We call them pterobreathers. For some frequencies the wings disappear and the solutions become exact moving breathers with no wings, showing the phenomenon of supertransmission of energy. We perform a theoretical analysis of pterobreathers in systems with substrate potential and show that they are characterized by a single frequency in the moving frame plus the frequency of the wings. We have also studied high-energy stationary breathers which transform into single and double kinks and stable multibreathers with very strong localization.

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Section: Introductionmentioning

confidence: 99%

Pterobreathers in a model for a layered crystal with realistic potentials: Exact moving breathers in a moving frame

2019

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“…There is also interest in the study of the possibility of excitation and propagation of solitons, discrete breathers and kinks in two-dimensional lattices. Different interatomic potentials, including discrete sine-Gordon and Lennard-Jones 27,28,45,46 and Morse 29,47 potentials, were used in these studies which confirm the existence and long lifetime of the kink solutions in two-dimensional lattices, including a two-dimensional model proposed for mica muscovite 27,28 . In the present work, we consider a one-dimensional lattice model which allows us to perform more rigorous study of the existence and stability of nonlinear excitations in a system with realistic interatomic potentials.…”

Section: Nonlinear Waves In Two-dimensional Latticesmentioning

confidence: 73%

Nonlinear waves in a model for silicate layers

Archilla

Zolotaryuk

Kosevich

et al. 2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Some layered silicates are composed of positive ions, surrounded by layers of ions with opposite sign. Mica muscovite is a particularly interesting material, because there exist fossil and experimental evidence for nonlinear excitations transporting localized energy and charge along the cation rows within the potassium layers. This evidence suggests that there are different kinds of excitations with different energies and properties. Some of the authors proposed recently a one-dimensional model based on physical principles and the silicate structure. The main characteristic of the model is that it has a hard substrate potential and two different repulsion terms, between ions and nuclei. In a previous work with this model, it was found the propagation of crowdions, i.e., lattice kinks in a lattice with substrate potential that transport mass and charge. They have a single specific velocity and energy coherent with the experimental data. In the present work, we perform a much more thorough search for nonlinear excitations in the same model using the pseudospectral method to obtain exact nanopteron solutions, which are single kinks with tails, crowdions, and bi-crowdions. We analyze their velocities, energies, and stability or instability and the possible reasons for the latter. We relate the different excitations with their possible origin from recoils from different beta decays and with the fossil tracks. We explore the consequences of some variation of the physical parameters because their values are not perfectly known. Through a different method, we also have found stationary and moving breathers, that is, localized nonlinear excitations with an internal vibration. Moving breathers have small amplitude and energy, which is also coherent with the fossil evidence.

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“…They can be produced by K + recoil, leaving behind a vacancy or anti-kink. Simulations have been done for 1D models, and at least in some models the kinks do not spread for a long distance [14,15]. Supersonic lattice kinks have only a discrete set of velocities and energies for which they do not radiate energy.…”

Section: A Lattice Kink or Crowdionmentioning

confidence: 99%

On the charge of quodons

Archilla¹,

Russell²

2016

LoM

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Muscovite mica is a mineral in which the tracks of charged swift particles, from radioactivity or cosmic rays, can be recorded and made visible by decoration with the mineral magnetite. Also, the tracks of quasi-one-dimensional lattice excitations, called quodons, moving along close-packed directions can be recorded. Most quodon tracks evolve from nuclear recoils following decay of the radioactive isotope . We analyze the possible results taking into account charge, energy and momentum conservation and considering the possible ionization states of the K atoms, which can be intrinsic localized modes, solitons, kinks or crowdions, travelling charge states and combinations of them.

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Numerical Simulations of Nonlinear Modes in Mica: Past, Present and Future

Cited by 25 publications

References 23 publications

Pterobreathers in a model for a layered crystal with realistic potentials: Exact moving breathers in a moving frame

Pterobreathers in a model for a layered crystal with realistic potentials: Exact moving breathers in a moving frame

Nonlinear waves in a model for silicate layers

On the charge of quodons

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